Problem: Simplify the following expression: $\dfrac{90k^3}{18k^3}$ You can assume $k \neq 0$.
Explanation: $ \dfrac{90k^3}{18k^3} = \dfrac{90}{18} \cdot \dfrac{k^3}{k^3} $ To simplify $\frac{90}{18}$ , find the greatest common factor (GCD) of $90$ and $18$ $90 = 2 \cdot 3 \cdot 3 \cdot 5$ $18 = 2 \cdot 3 \cdot 3$ $ \mbox{GCD}(90, 18) = 2 \cdot 3 \cdot 3 = 18 $ $ \dfrac{90}{18} \cdot \dfrac{k^3}{k^3} = \dfrac{18 \cdot 5}{18 \cdot 1} \cdot \dfrac{k^3}{k^3} $ $\phantom{ \dfrac{90}{18} \cdot \dfrac{3}{3}} = 5 \cdot \dfrac{k^3}{k^3} $ $ \dfrac{k^3}{k^3} = \dfrac{k \cdot k \cdot k}{k \cdot k \cdot k} = 1 $ $ 5 \cdot 1 = 5 $